(3x+4)(3x+4)=80

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Solution for (3x+4)(3x+4)=80 equation:


Simplifying
(3x + 4)(3x + 4) = 80

Reorder the terms:
(4 + 3x)(3x + 4) = 80

Reorder the terms:
(4 + 3x)(4 + 3x) = 80

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) = 80
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 80
((16 + 12x) + 3x * (4 + 3x)) = 80
(16 + 12x + (4 * 3x + 3x * 3x)) = 80
(16 + 12x + (12x + 9x2)) = 80

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) = 80

Solving
16 + 24x + 9x2 = 80

Solving for variable 'x'.

Reorder the terms:
16 + -80 + 24x + 9x2 = 80 + -80

Combine like terms: 16 + -80 = -64
-64 + 24x + 9x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-64 + 24x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-7.111111111 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + 2.666666667x + 7.111111111 + x2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + 2.666666667x + x2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 7.111111111
2.666666667x + x2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
2.666666667x + x2 = 7.111111111

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 7.111111111 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 7.111111111 + 1.777777780

Combine like terms: 7.111111111 + 1.777777780 = 8.888888891
1.777777780 + 2.666666667x + x2 = 8.888888891

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 8.888888891

Calculate the square root of the right side: 2.98142397

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 2.98142397 and -2.98142397.

Subproblem 1

x + 1.333333334 = 2.98142397 Simplifying x + 1.333333334 = 2.98142397 Reorder the terms: 1.333333334 + x = 2.98142397 Solving 1.333333334 + x = 2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 2.98142397 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 2.98142397 + -1.333333334 x = 2.98142397 + -1.333333334 Combine like terms: 2.98142397 + -1.333333334 = 1.648090636 x = 1.648090636 Simplifying x = 1.648090636

Subproblem 2

x + 1.333333334 = -2.98142397 Simplifying x + 1.333333334 = -2.98142397 Reorder the terms: 1.333333334 + x = -2.98142397 Solving 1.333333334 + x = -2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -2.98142397 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -2.98142397 + -1.333333334 x = -2.98142397 + -1.333333334 Combine like terms: -2.98142397 + -1.333333334 = -4.314757304 x = -4.314757304 Simplifying x = -4.314757304

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.648090636, -4.314757304}

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